We discuss the problem of homotopy-type reconstruction of compact shapes that are in the intrinsic length metric. The reconstructed spaces are Vietoris–Rips complexes computed from a compact sample , Hausdorff–close to the unknown shape . Instead of the Euclidean metric on the sample, our reconstruction technique leverages a path-based metric to compute these complexes. As naturally emerging in the reconstruction framework, we also study the Gromov–Hausdorff topological stability and finiteness problem for general compact spaces. Our techniques provide novel sampling conditions as an alternative to the existing and commonly used techniques using weak feature size and –reach. In particular, we introduce a new parameter, called the restricted distortion, which is a generalization of the well-known global distortion of embedding. We show examples of Euclidean subspaces, for which the known parameters such as the reach, –reach and weak features size vanish, whereas the restricted distortion is finite, making our reconstruction results applicable for such spaces.